Problem: Simplify the following expression: $k = \dfrac{11x + 66}{11x - 77}$ You can assume $x \neq 0$.
Explanation: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $11x + 66 = (11 \cdot x) + (2\cdot3\cdot11)$ The denominator can be factored: $11x - 77 = (11 \cdot x) - (7\cdot11)$ The greatest common factor of all the terms is $11$ Factoring out $11$ gives us: $k = \dfrac{(11)(x + 6)}{(11)(x - 7)}$ Dividing both the numerator and denominator by $11$ gives: $k = \dfrac{x + 6}{x - 7}$